I played GW Kill Team last night and the rules do specify that each model acts independently during the game. I played IG against Savion47's CSM and it was a good time. My horrible dice rolling had me losing more models to cultists pistols than anything else, it was pretty hilarious. So yeah, my boys got whipped.
We're going to give it another go next week using the HoR Kill Team rules, I will definitely be playing a different army.
I am intrigued by the HoR rules and am looking forward to our game. One thing I do like about GW's version is if I am using Orks I can have a nob squad make up my kill team but it does not look like that is an option with HoR rules.